Economics Chapter 03 The repair costs for five cars which were crashed by a safety

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Ch.3 NumericallySummarizingData

3.1 MeasuresofCentralTendency

1 Determinethearithmeticmean,median,andmodeofavariablefromrawdata.

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

1) Findthemean,median,andmodeofthefollowingstatisticstudentsʹtestscores:

71 74 67 71 64 72 71 65 66 69

2) Calculatethemean,median,andmodeforthefollowingsample:5,10,6,11,1

1

10,1.

3) Calculatethemean,median,andmodeforthefollowingsample:5,10,6,100,0,0,10,0.

4) Thehightemperatures(indegreesCelsius)eachdayoverathreeweekperiodwereasfollows:17,18,20,22,

21,19,16,15,18,20,21,21,22,21,19,20,19,17,16,16,17.Computethemean,median,andmode.

5) Inasampleof18studentsatEastHighSchoolthefollowingnumberofdaysofabsenceswererecordedforthe

previoussemester:4,3,1,0,4,2,3,0,1,2,3,0,4,1,1,5,1,1.Computethemean,median,andmode.

6) Thenumberofgoalsscoredbyarandomsampleof16hockeyplayersforagivenseasonare5,3,21,10,7,2,0,

30,19,6,4,7,10,5,7,and24.Computethemean,median,andmode.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

7) Theheightsoftenfemalestudents(ininches)inacollegemathclassarelistedbelow.Findthemean.

65 66 67 66 67 70 67 70 71 68

A) 67.7inches B) 65.5inches C) 71.1inches D) 70.0inches

8) Theheightsoftenmalestudents(ininches)inacollegebiologyclassarelistedbelow.Findthemean.

71 67 67 72 76 72 73 68 72 72

A) 71inches B) 67inches C) 68inches D) 72inches

9) Therepaircostsforfivecarswhichwerecrashedbyasafetytestingorganizationwereasfollows:

$100,$150,$200,$250,and$150.Findthemeancostofrepair.

A) $170 B) $160 C) $180 D) $140

10) Eachyearadvertisersspendbillionsofdollarspurchasingcommercialtimeonnetworksportstelevision.Inthe

first6monthsof1988,advertisersspent$1.1billion.Arecentarticlelistedthetop10leadingspenders(in

millionsofdollars):

CompanyA$70.3 CompanyF$26.4

CompanyB60.5 CompanyG24.6

CompanyC57.9 CompanyH21.1

CompanyD54.7 CompanyI22.4

CompanyE29.3 CompanyJ20.9

Calculatethemeanamountspent.

A) 38.81milliondollars B) 19.52 milliondollars

C) 381.01milliondollars D) 49.40 milliondollars

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11) Thenumberofstudentsenrolledinaphysicsclassforthelasttensemestersarelistedbelow.Findthemedian

numberofstudents.

65 66 67 66 67 70 67 70 71 68

A) 67students B) 66students C) 68students D) 70students

12) Thecommutingtimes(inminutes)ofanemployeefortenconsecutivedaysarelistedbelow.Findthemedian

commute.

71 67 67 72 76 72 73 68 72 72

A) 72minutes B) 67minutes C) 71minutes D) 73minutes

13) Thefollowingdatarepresentsarandomsampleof15complaintsregisteredwiththecustomerservice

departmentofastore.Determinethemediancomplaint.

Other defectiveproduct excessivewaitingtime

Messystore other other

Messystore other messystore

Other messystore messystore

Defectiveproduct other messystore

A) Nomedian B) Messystore

C) Defectiveproduct D) Excessivewaitingtime

14) Eachyearadvertisersspendbillionsofdollarspurchasingcommercialtimeonnetworksportstelevision.Inthe

first6monthsoftheyear,advertisersspent$1.1billion.Arecentarticlelistedthetop10leadingspenders(in

millionsofdollars):

CompanyA$73.2 CompanyF$24.6

CompanyB61.7 CompanyG24.4

CompanyC57 CompanyH23.9

CompanyD56.4 CompanyI23

CompanyE28.5 CompanyJ19.2

Calculatethemedian.

A) 26.55milliondollars B) 5.15 milliondollars

C) 39.19milliondollars D) 54.00 milliondollars

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

15) Thenumberofyardsthatafootballplayerrushedinthefirst13gamesofhisNFLcareerarelistedbelow.Find

themeanandmediannumberofyardsrushed.Roundthemeantothenearestwholenumber.

Whichmeasureofcentraltendency–themeanorthemedian–betterrepresentsthedata?Explainyour

reasoning.

349 32 33 39 22 42 9939 52 58 70

16) Thenumberofhomeworkpointsearnedbytwelvestudentsinahistoryclassoveronetermarelistedbelow.

Findthemeanandmediannumberofpoints.Roundthemeantothenearestwholenumber.Whichmeasureof

centraltendency–themeanorthemedian–bestrepresentsthedata?Explainyourreasoning.

102 56 25 9956 165 88 122 150 91 114

17) Theannualprofitsofteninternetbusinessesarelistedbelow.Findthemeanandmedianprofits.Roundthe

mediantothenearestdollar.Whichmeasure–themeanorthemedian–bestrepresentsthedata?Explainyour

reasoning.

$1,172,246 $163,659 $440,584 $350,634 $290,596

$186,731 $145,809 $143,209 $139,096 $125,106

Page55

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

18) Thecommutingtimesoftenemployees(inminutes)arelistedbelow.Findthemodescore.

65 66 67 66 67 70 67 70 71 68

A) 67minutes B) 65minutes C) 66minutes D) 68minutes

19) TheFebruaryutilitybills(indollars)fortenresidentsofalargecityarelistedbelow.Findthemodeamount.

71 67 67 72 76 72 73 68 72 72

A) $72 B) $67 C) $76 D) $73

20) ThefollowingdatarepresentthebachelordegreesofCEOʹsatareasmallbusinesses.Determinethemode

degree.

Degree Number

Accounting 29

Business 42

LiberalArts 5

Marketing 24

Other 7

usiness B) accounting C) marketing D) nomode

21) Thefollowingdatarepresentarandomsampleof15complaintsregisteredwiththecustomerservice

departmentofastore.Determinethemodecomplaint.

defectiveproduct rudepersonnel messystore

other defectiveproduct defectiveproduct

other excessivewaitingtime other

defectiveproduct other other

rudepersonnel defectiveproduct other

A) other B) defectiveproduct C) messystore D) nomode

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

22) Theaccompanyingdatasetcontainsquizscoresfor12studentsinachemistryclass:18,15,5,8,15,20,2,16,10,

12,20,15.

a.Findameasureofcentraltendencythatseparatesthedataintotwogroupssuchthateachgroup

consistsof50%ofthescoresaboveand50%ofthescoresbelowthatmeasure.

b.Findameasureofcentraltendencythatrepresentsthequizscorethatoccursmostoften.

c.Findameasureofcentraltendencythatrepresentstheaverageofthe12quizscores.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

23) IfX1

X2

X3

…,XNaretheNobservationsofavariablefromapopulation,thenthepopulationmeanis

symbolizedby

A) μB) XC) ΣD) X

24) Anumericalsummaryofapopulationisa

A) Parameter B) Statistic

C) Variable D) Qualitativeresponse

25) Themedianofadatasetforavariableisthedatavaluethat

A) Liesinthemiddleofthedatawhenthedataisarrangedinascendingorder.

B) Appearsthemostoften

C) Istheaverage,thatis,thesumofallthedatavaluesofthevariabledividedbythenumberofobservations

inthedataset?

D) Noneofthese

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26) The________ofavariableiscomputedbydeterminingthesumofallthevaluesofthevariableinthedataset

anddividingthissumbythenumberofobservationsinthedataset.

A) Arithmeticmean B) Median C) Mode D) Geometricmean

27) Whichmeasureofcentraltendencymaynotexistforallnumericdatasets?

A) Mode B) Median C) Mean D) Midrange

28) Whichmeasureofcentraltendencymayhavemorethanonevalueinanumericdataset?

A) Mode B) Median C) Mean D) Midrange

29) Whichmeasureofcentraltendencyisnotresistanttoextremevaluesinanumericdataset?

A) Mean B) Mode C) Median D) Parameters

2 Explainwhatitmeansforastatistictoberesistant.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Describetheshapeofthehistogram.Thedataset:Pick–Threelotteryresultsfor10consecutiveweeks

3676061784

1575915399

2230884024

A) uniform B) symmetric

C) skewedtotheleft D) skewedtotheright

2) Describetheshapeofthehistogram.Thedataset:ageof20householdstereosystemsrandomlyselected

fromaneighborhood

12 64911 17898

913 515 768821

A) symmetric B) uniform

C) skewedtotheleft D) skewedtotheright

3) Describetheshapeofthehistogram.Thedataset:round–tripcommutingtimes(inminutes)of20randomly

selectedemployees

135 120 115 132 136 124 119 145 98 110

125 120 115 130 140 105 116 121 125 108

A) skewedtotheright B) uniform

C) skewedtotheleft D) symmetric

4) Thedistributionofsalariesofprofessionalbasketballplayersisskewedtotheright.Whichmeasureofcentral

tendencywouldbethebestmeasuretodeterminethelocationofthecenterofthedistribution?

A) median B) mode C) mean D) frequency

Page57

Forthedistributiondrawnhere,identifythemean,median,andmode.

A) A=mode,B=median,C=mean B) A=median,B=mode,C=mean

C) A=mode,B=mean,C=median D) A=mean,B=mode,C=median

6) Indistributionsthatareskewedtotheright,whatistherelationshipofthemean,median,andmode?

A) mean>median>mode B) median>mean>mode

C) mode>median>mean D) mode>mean>median

7) Indistributionsthatareskewedtotheleft,whatistherelationshipofthemean,median,andmode?

A) mode>median>mean B) mean>median>mode

C) mode<mean<median D) mode>mean>median

8) Manyfirmsuseon–the–

obtrainingtoteachtheiremployeesnewsoftware.Supposeyouworkinthepersonnel

departmentofafirmthatjustfinishedtrainingagroupofitsemployeesinnewsoftware,andyouhavebeen

requestedtoreviewtheperformanceofoneofthetraineesonthefinaltestthatwasgiventoalltrainees.The

meanofthetestscoresis76.Additionalinformationindicatedthatthemedianofthetestscoreswas83.What

typeofdistributionmostlikelydescribestheshapeofthetestscores?

A) skewedtotheleft B) symmetric

C) skewedtotheright D) unabletodeterminewiththeinformationgiven

9) Aseveredroughtaffectedseveralwesternstatesfor3years.AChristmastreefarmerisworriedaboutthe

droughtʹseffectonthesizeofhistrees.Todecidewhetherthegrowthofthetreeshasbeenretarded,thefarmer

decidestotakeasampleoftheheightsof25treesandobtainsthefollowingresults(recordedininches):

60 57 62 69 46 54 64 60 59 58 75 51 49

67 65 44 58 55 48 62 63 73 52 55 50

Whichmeasureofcentraltendencywouldbeconsideredthebestmeasuretouseinthisproblem?

A) mean B) median C) mode D) range

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

10) Parkingatalargeuniversityhasbecomeaverybigproblem.Universityadministratorsareinterestedin

determiningtheaverageparkingtime(e.g.thetimeittakesastudenttofindaparkingspot)ofitsstudents.An

administratorinconspicuouslyfollowed140studentsandcarefullyrecordedtheirparkingtimes.Theparking

timesrecordedfollowedadistributionthatwasskewedtotheright.Basedonthisinformation,discussthe

relationshipbetweenthemeanandthemedianforthe140studentparkingtimescollected.

Page58

11) Theoutputbelowgivesthemeanandmedianforthenationaldropoutratesofhighschoolstudentsin2010

and2012.

Drop2010 Drop2012

N5151

MEAN 28.38 26.76

MEDIAN 27.94 25.54

Usethesampleinformationtodeterminetheshapeofthedistributionsofthehighschooldropoutratesin2010

and2012.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

12) Theannualprofitsoffivelargecorporationsinacertainareaaregivenbelow.Whichmeasureofcentral

tendencyshouldbeused?

$135,000 $143,000 $163,000 $133,000 $1,213,000

A) median B) mean C) mode D) midrange

13) Ifthegraphofadistributionofdatashowsthatthegraphisskewedtotherightthenthe

A) Mean>Median

B) Mean≈Median

C) Mean<Median

D) Noconclusionabouttherelativepositionofthemeanandthemediancanbemade

14) Ifthegraphofadistributionofdatashowsthatthegraphisskewedtotheleftthenthe

A) Median>Mean

B) Mean≈Median

C) Mean>Median

D) Noconclusionabouttherelativepositionofthemeanandthemediancanbemade

15) Ifthegraphofadistributionofdatashowsthatthegraphissymmetricthenthe

A) Meanisabettermeasureofcentraltendency

B) Medianisabettermeasureofcentraltendency

C) Modeisabettermeasureofcentraltendency

D) Midrangeisabettermeasureofcentraltendency

16) Whichmeasureofcentraltendencyismorerepresentativeofthetypicalobservationifthegraphofthedatais

skewedtotheright?

A) Median B) Mean C) Mode D) Midrange

17) Whichmeasureofcentraltendencyismorerepresentativeofthetypicalobservationifthegraphofthedatais

skewedtotheleft?

A) Median B) Mean C) Mode D) Midrange

3.2 MeasuresofDispersion

1 Determinetherange,standarddeviation,andvarianceofavariablefromrawdata.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Computetherangeforthesetofdata.

1) 13

14

15

16

17

A) 4 B) 17 C) 0.8 D) 13

Page59

2) 3

3

17

29

A) 26 B) 16.1 C) 17 D) 169.1

3) 9

20

9

20

9

20

9

20

A) 11 B) 20 C) 14.5 D) 22

4) 8

19

2

13

9

A) 17 B) 19 C) 2 D) 1

5) 25

34

13

42

52

A) 39 B) 52 C) 13 D) 33.2

6) 9

9

7

1

6

10

9

7

9

A) 9 B) 10 C) 7.4 D) 11

7) 67

140

25

90

176

A) 151 B) 176 C) 25 D) 99.6

8) 112

494

230

565

401

257

A) 453 B) 565 C) 112 D) 343.2

9) 2.8

5.8

1.6

4.4

6.7

3.8

A) 5.1 B) 6.7 C) 1.6 D) 4.2

10) 0.23

0.12

0.554

0.379

0.575

0.257

A) 0.455 B) 0.575 C) 0.12 D) 0.353

Findthesamplestandarddeviation.

11) 15

16

17

18

19

A) 1.6 B) 2.5 C) 1.3 D) 1.5

12) 11

11

14

17

A) 3 B) 2.8 C) 7.7 D) 9.0

13) 19

16

17

12

8

7

16

9

12

A) 4.3 B) 4.1 C) 18.6 D) 16.5

14) 88

87

21

86

38

44

43

47

80

A) 25.7 B) 23.0 C) 589.3 D) 530.4

15) 262

296

116

174

162

287

220

287

201

A) 64.3 B) 60.6 C) 4138.2 D) 3678.4

16) 11

5

11

13

16

13

19

12

19

A) 4.1 B) 3.8 C) 1.5 D) 3.6

17) 4

1

8

14

7

12

16

17

10

A) 5.4 B) 5.1 C) 29.4 D) 26.1

Provideanappropriateresponse.

18) TheAprilprecipitationamounts(ininches)for10citiesarelistedbelow.Findtherangeofthedata.

2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

A) 3.2inches B) 2.45inches C) 1.4inches D) 2.8inches

Page60

19) TheJanuaryutilitybills(indollars)for20residentsofalargecityarelistedbelow.Findtherangeofthedata.

70 72 71 70 69 73 69 68 70 71

67 71 70 74 69 68 71 71 71 72

A) $7 B) $2.98 C) $2 D) $1.73

20) Thecosts(indollars)of10collegemathtextbooksarelistedbelow.Findthesamplestandarddeviation.

70 72 71 70 69 73 69 68 70 71

A) $1.49 B) $70.30 C) $5.00 D) $2.23

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

21) Thecosts(indollars)of10collegemathtextbooksarelistedbelow.Findthepopulationstandarddeviation

andthepopulationvariance.

70 72 71 70 69 73 69 68 70 71

22) Inarandomsample,10employeesatalocalplantwereaskedtocomputethedistancetheytraveltoworkto

thenearesttenthofamile.Thedataislistedbelow.Computetherange,samplestandarddeviationandsample

varianceofthedata.

1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0.8

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

23) Thetopspeeds(inmph)forasampleoffivenewautomobilebrandsarelistedbelow.Calculatethestandard

deviationofthespeeds.

160,125,190,185,105

A) 37.2mph B) 28,458.00 mph C) 153.00 mph D) 85mph

24) Overthelast10yearsfourmutualfundsallhadthesamemeanrateofreturn,12%.Thesemutualfundshad

differentstandarddeviationsasfollows:MutualMoney8%,Co–joinedInvestments6%,TogetherFund4%,All

forOneFund9%.Whichmutualfundinvestmentisthemostconsistentinrateofreturn?

A) TogetherFund B) MutualMoney

C) Co–

oinedInvestments D) AllforOneFund

25) Thebookcost(indollars)foronesemesterʹsbooksaregivenbelowforasampleoffivecollegestudents.

Calculatethesamplevarianceofthebookcosts.

200,130,400,500,345

A) 22,450.00 B) 149.83 C) 370.00 D) 315.00

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

26) Theagesoffiverandomlyselectedstudentsinthebiologydepartmentataprivateuniversityare30

26

27

25

and29.Calculatethesamplevarianceoftheseages.

Page61

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

27) Eachyearadvertisersspendbillionsofdollarspurchasingcommercialtimeonnetworksportstelevision.Inthe

first6monthsof1988,advertisersspent$1.1billion.Whowerethelargestspenders?Inarecentarticle,listed

thetop10leadingspenders(inmillionofdollars):

CompanyA$70.7 CompanyF$27.3

CompanyB60.7 CompanyG26.1

CompanyC55.4 CompanyH22.8

CompanyD54.8 CompanyI23

CompanyE28.7 CompanyJ19.4

Calculatethesamplevariance.

A) 367.36 B) 19.17 C) 38.89 D) 51.30

28) Inthecomputationofthesamplestandardvariance,howmanydegreesoffreedomarethereinadatasetthat

has15datavalues?

A) 14 B) 15 C) 16 D) noneofthese

29) Forthedatasetgivenbelowthesamplevariancewillbecomputed.Howmanydegreesoffreedomarethere?

6961511 598

A) 8 B) 9 C) 1 D) 10

30) Lastyearbattingaveragesinprofessionalbaseballaveraged0.266 withahighof0.334andalowof0.228

(minimum250at–bats).Basedonthisinformation,whichmeasureofvariationcouldbecalculated?

A) range B) variance

C) standarddeviation D) percentile

31) Whichisnotameasureofdispersion?

A) Mean B) Standarddeviation

C) Variance D) Range

32) The_______________istheeasiestmeasureofdispersiontocalculate.

A) Range B) Standarddeviation

C) Variance D) Meanabsolutedeviation

33) TrueorFalse:Thevarianceofapopulationisthearithmeticaverageofthesquareddeviationsaboutthe

populationmean.

A) True B) False

34) TrueorFalse:Varianceisthesquarerootofstandarddeviation.

A) False B) True

35) Astatisticissaidtobebiasedifit

A) Systematicallyunderestimatesoroverestimatesaparameter

B) Hasexactlythesamevalueastheparameter

C) Isdeterminedfromatrimmedsample

D) Leadstoanerroneousconclusionaboutthesample

Page62

2 UsetheEmpiricalRuletodescribedatathatarebellshaped.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Atatennistournamentastatisticiankeepstrackofeveryserve.Thestatisticianreportedthatthemeanserve

speedofaparticularplayerwas104milesperhour(mph)andthestandarddeviationoftheservespeedswas8

mph.Assumethatthestatisticianalsogaveustheinformationthatthedistributionoftheservespeedswasbell

shaped.Whatproportionoftheplayerʹsservesareexpectedtobebetween112mphand120mph?

A) 0.1350 B) 0.270 C) 0.95 D) 0.68

2) TheamountoftelevisionviewedbytodayʹsyouthisofprimaryconcerntoParentsAgainstWatching

Television(PAWT).300parentsofelementaryschool–agedchildrenwereaskedtoestimatethenumberof

hoursperweekthattheirchildwatchedtelevision.Themeanandthestandarddeviationfortheirresponses

were16and4,respectively.PAWTconstructedastem–and–leafdisplayforthedatathatshowedthatthe

distributionoftimeswasabell–shapeddistribution.Giveanintervalaroundthemeanwhereyoubelievemost

(approximately95%)ofthetelevisionviewingtimesfellinthedistribution.

etween8and24hoursperweek B) lessthan12 andmorethan20hoursperweek

etween4and28hoursperweek D)

etween12 and20hoursperweek

3) Healthcareissuesarereceivingmuchattentioninbothacademicandpoliticalarenas.Asociologistrecently

conductedasurveyofcitizensover60yearsofagewhosenetworthistoohightoqualifyforgovernment

healthcarebutwhohavenoprivatehealthinsurance.Theagesof25uninsuredseniorcitizenswereasfollows:

68 73 66 76 86 74 61 89 65 90 69 92 76

62 81 63 68 81 70 73 60 87 75 64 82

Supposethemeanandstandarddeviationare74.0and9.7,respectively.Ifweassumethatthedistributionof

agesisbellshaped,whatpercentageoftherespondentswillbebetween64.3and93.4yearsold?

A) approximately81.5% B) approximately68%

C) approximately95% D) approximately83.9%

4) Asmallcomputingcenterhasfoundthatthenumberofjobssubmittedperdaytoitscomputershasa

distributionthatisapproximatelybellshaped,withameanof84jobsandastandarddeviationof10.Wheredo

weexpectmost(approximately95%)ofthedistributiontofall?

etween64and104jobsperday B)

etween74 and94jobsperday

etween54and114jobsperday D)

etween64 and114jobsperday

5) Astudywasdesignedtoinvestigatetheeffectsoftwovariables–(1)astudentʹslevelofmathematicalanxiety

and(2)teachingmethod–onastudentʹsachievementinamathematicscourse.Studentswhohadalowlevel

ofmathematicalanxietyweretaughtusingthetraditionalexpositorymethod.Thesestudentsobtainedamean

scoreof460withastandarddeviationof50onastandardizedtest.Assumingabell–shapeddistribution,what

percentageofscoresexceeded360?

A) approximately97.5% B) approximately95%

C) approximately2.5% D) approximately84%

6) Astudywasdesignedtoinvestigatetheeffectsoftwovariables–(1)astudentʹslevelofmathematicalanxiety

and(2)teachingmethod–onastudentʹsachievementinamathematicscourse.Studentswhohadalowlevel

ofmathematicalanxietyweretaughtusingthetraditionalexpositorymethod.Thesestudentsobtainedamean

scoreof460withastandarddeviationof40onastandardizedtest.Assumingabell–shapeddistribution,

wherewouldapproximately68%ofthestudentsscore?

etween420and500 B)

etween380 and540

elow380orabove540 D)

elow420 orabove500

Page63

7) Solarenergyisconsideredbymanytobetheenergyofthefuture.Arecentsurveywastakentocomparethe

costofsolarenergytothecostofgasorelectricenergy.Resultsofthesurveyrevealedthatthedistributionof

theamountofthemonthlyutilitybillofa3–bedroomhouseusinggasorelectricenergyhadameanof$120

andastandarddeviationof$11.Ifthedistributioncanbeconsideredbellshaped,whatpercentageofhomes

willhaveamonthlyutilitybillofmorethan$109?

A) approximately84% B) approximately95%

C) approximately16% D) approximately32%

8) Manyfirmsuseon–the–

obtrainingtoteachtheiremployeesnewsoftware.Supposeyouworkinthepersonnel

departmentofafirmthatjustfinishedtrainingagroupofitsemployeesinnewsoftware,andyouhavebeen

requestedtoreviewtheperformanceofoneofthetraineesonthefinaltestthatwasgiventoalltrainees.The

meanandstandarddeviationofthetestscoresare80and3,respectively,andthedistributionofscoresisbell

shaped.Whatpercentageoftest–takersscoredbetterthanatraineewhoscored71?

A) approximately99.85% B) approximately84%

C) approximately95% D) approximately97.5%

9) Aseveredroughtaffectedseveralwesternstatesfor3years.AChristmastreefarmerisworriedaboutthe

droughtʹseffectonthesizeofhistrees.Todecidewhetherthegrowthofthetreeshasbeenretarded,thefarmer

decidestotakeasampleoftheheightsof25trees.Typicallytreesofthisagehaveameanheightof65inches

withastandarddeviationof9inches.Assumingthedistributionisbellshaped,wheredoyouexpectmiddle

95%ofthetreeheightstofall?

etween47and83inchestall B)

etween56and74inchestall

etween38and92inchestall D) over56inchestall

10) Thescoresfromastatestandardizedtest haveabell–shapeddistributionwithameanof100andastandard

deviationof15.UsetheEmpiricalRuletofindthepercentageofstudentswithscoresbetween70and130.

A) 95% B) 68% C) 99.7% D) 100%

11) Thescoresfromastatestandardizedtest haveameanof80andastandarddeviationof10.Thedistributionof

thescoresisroughlybellshaped.UsetheEmpiricalRuletofindthepercentageofscoresthatliebetween60

and80.

A) 47.5% B) 68% C) 34% D) 95%

12) Theaveragescoreoflocalstudentsonacollegeentranceexamis110,withastandarddeviationof5.The

distributionisroughlybellshaped.UsetheEmpiricalRuletofindthepercentageoflocalstudentswithscores

above120.

A) 2.5% B) 5% C) 95% D) 97.5%

3 UseChebyshevʹsinequalitytodescribeanysetofdata.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Atatennistournamentastatisticiankeepstrackofeveryserve.Thestatisticianreportedthatthemeanserve

speedofaparticularplayerwas98milesperhour(mph)andthestandarddeviationoftheservespeedswas14

mph.Ifnothingisknownabouttheshapeofthedistribution,giveanintervalthatwillcontainthespeedsofat

leasteight–ninthsoftheplayerʹsserves.

A) 56mphto140mph B) 70 mphto126 mph

C) 42mphto154mph D) 140 mphto182 mph

Page64

2) Astudywasdesignedtoinvestigatetheeffectsoftwovariables–(1)astudentʹslevelofmathematicalanxiety

and(2)teachingmethod–onastudentʹsachievementinamathematicscourse.Studentswhohadalowlevel

ofmathematicalanxietyweretaughtusingthetraditionalexpositorymethod.Thesestudentsobtainedamean

scoreof480withastandarddeviationof20onastandardizedtest.Assumingnoinformationconcerningthe

shapeofthedistributionisknown,whatpercentageofthestudentsscoredbetween440and520?

A) atleast75% B) approximately95%

C) atleast88.9% D) approximately68%

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

3) Commutingtimesforemployeesofalocalcompany haveameanof63.6minutesandastandarddeviationof

2.5minutes.WhatdoesChebyshevʹsTheoremsayaboutthepercentageofemployeeswithcommutingtimes

between58.6minutesand68.6minutes?

4) Commutingtimesforemployeesofalocalcompany haveameanof63.6minutesandastandarddeviationof

2.5minutes.WhatdoesChebyshevʹsTheoremsayaboutthepercentageofemployeeswithcommutingtimes

between56.1minutesand71.1minutes?

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

5) Fillintheblank.____________givesusamethodofinterpretingthestandarddeviationthatappliestoanydata

set,regardlessoftheshapeofthedistribution.

A) Chebyshevʹsrule B) TheEmpiricalRule

C) Chebyshevʹsruleandtheempiricalrule D) noneofthese

6) Fillintheblank.____________isamethodofinterpretingthestandarddeviationthatappliestodatathathave

abell–shapeddistribution.

A) TheEmpiricalRule B) Chebyshevʹsrule

C) Chebyshevʹsruleandtheempiricalrule D) noneofthese

7) Ifnothingisknownabouttheshapeofadistribution,whatpercentageoftheobservationsfallwithin2

standarddeviationsofthemean?

A) atleast75% B) atmost25%

C) approximately95% D) approximately5%

3.3 MeasuresofCentralTendencyandDispersionfromGroupedData

1 Approximatethemeanandstandarddeviationofavariablefromgroupeddata.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Forthefollowingdata,approximatethemeannumberofunusedvacationdaysattheendoftheyear.

Days Frequency

1–22

3–421

5–620

7–810

9–10 30

A) 6.6 B) 6.1 C) 7.1 D) 7.8

Page65

2) Forthefollowingdata,approximatethemeannumberofemailsreceivedperday.

Emails(perday) Frequency

8–11 3

12–15 34

16–19 31

20–23 8

24–27 27

A) 18.4 B) 17.9 C) 16.9 D) 19.9

3) Forthefollowingdata,approximatethemeanweeklygrocerybill.

Bill(indollars) Frequency

135–139 13

140–144 7

145–149 11

150–154 18

155–159 9

A) $147.30 B) $145.30 C) $149.30 D) $145.80

4) Onarecentdayduringthefluseason,theMidtownMedicalClinicsawmanypatients.Patientshadtheir

temperatures(in°F)taken.Thedistributionoftemperaturesisgivenbelow.Determinethemeantemperature

ofasampleof100patients.

Temperatures Frequency

95.6–96.49 1

96.5–97.39 3

97.4–98.29 19

98.3–99.19 28

99.2–100.09 35

100.1–100.99 12

101.0–101.89 2

A) 99.08°F B) 99.52°F C) 98.75°F D) 98.63°F

5) A1–poundbagofpeanutscontains430peanuts.Thedistributionofweightsingramsofthepeanutsisgiven

below.Whatisthemeanweightofapeanut?

Weights

(grams)

Frequency

0.755–0.814 3

0.815–0.874 2

0.875–0.934 2

0.935–0.994 2

0.995–1.054 168

1.055–1.114 241

1.115–1.174 12

A) 1.059g B) 1.088g C) 0.965g D) 1.029g

Page66

6) Forthefollowingdataset,approximatethesamplestandarddeviationofunusedvacationdays.

Days Frequency

1–29

3–422

5–628

7–815

9–10 14

A) 2.4days B) 5.5days C) 3.5days D) 5.9days

7) Forthefollowingdataset,approximatethesamplestandarddeviationofemailsperday.

Emails(perday) Frequency

8–11 18

12–15 23

16–19 38

20–23 47

24–27 32

A) 5.1emails B) 4.0emails C) 25.8emails D) 19.3emails

8) Forthefollowingdataset,approximatethesamplestandarddeviationofcommutingtimesperday.

Commute(inmin) Frequency

50–52 5

53–55 8

56–58 12

59–61 13

62–64 11

A) 3.9min B) 6.6min C) 2.5min D) 55.7min

9) Forthefollowingdataset,approximatethesamplestandarddeviationofunusedvacationdays.

Days Frequency

1–29

3–412

5–68

7–85

9–10 4

A) 2.6days B) 2.5days C) 6.5days D) 6.6days

10) Forthefollowingdataset,approximatethesamplestandarddeviationofdistancesfromwork(inmiles).

Distance(miles) Frequency

8–11 15

12–15 21

16–19 36

20–23 39

24–27 23

A) 4.9miles B) 24.5miles C) 5.2miles D) 24.3miles

Page67

11) Forthefollowingdataset,approximatethesamplestandarddeviationofmonthlytelephonebills(indollars).

Bill(in$) Frequency

50–52 2

53–55 5

56–58 12

59–61 19

62–64 7

A) $3.11 B) $58.60 C) $93.12 D) $9.65

12) Onarecentdayduringthefluseason,theMidtownMedicalClinicsawmanypatients.Patientshadtheir

temperaturestaken(in°F).Thedistributionoftemperaturesisgivenbelow.Determinethestandarddeviation

ofthetemperaturesofasampleof100patients.

Temperatures Frequency

95.6–96.49 1

96.5–97.39 3

97.4–98.29 19

98.3–99.19 28

99.2–100.09 35

100.1–100.99 12

101.0–101.89 2

A) 1.021°F B) 1.031°F C) 1.015°F D) 1.04°F

13) A1–poundbagofpeanutscontained430peanuts.Thedistributionofweights(ingrams)ofthepeanutsis

givenbelow.Whatisthesamplestandarddeviationoftheweightofapeanut?

Weights

(grams)

Frequency

0.755–0.814 3

0.815–0.874 2

0.875–0.934 2

0.935–0.994 2

0.995–1.054 168

1.055–1.114 241

1.115–1.174 12

A) 0.045g B) 0.002g C) 0.209g D) 0.000004g

2 Computetheweightedmean.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Astudentreceivestestscoresof62,83,and91.Thestudentʹstermprojectscoreis88andherhomeworkscore

is76.Eachtestisworth20%ofthefinalgrade,thetermprojectis25%ofthefinalgrade,andthehomework

gradeis15%ofthefinalgrade.Whatisthestudentʹsmeanscoreintheclass?

A) 80.6 B) 76.6 C) 83.3 D) 80.0

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2) Thegradesaregivenforastudentforaparticularterm.Findthegradepointaverage.Thepointvaluesof

gradesaregivenbelow.

A:4, B:3, C:2, D:1, F:0

GradeCreditHours

C3

F1

D2

F2

F3

A) 0.73 B) 2.2

C) 0.6 D) 1.8

3) Inahealthfoodstore,JennyandKevincreateatrailmixfromdriedfruit,nuts,andgranola.Theybuy5

poundsofdriedfruitat$4.00perpound,4poundsofnutsat$5.00perpound,and2poundsofgranolaat

$3.50perpound.Determinethecostperpoundofthemix.

A) $4.27 B) $3.76 C) $4.47 D) $4.39

imbuyshisschoolsuppliesinbulk.Ononeparticularshoppingtriphebought5redpensat$1.29each,3blue

pensat$1.49each,6greenpensat$1.79eachand9blackpensat$0.99each.Whatwastheaveragecostofa

pen?

A) $1.33 B) $1.29 C) $0.99 D) $1.39

3.4 MeasuresofPositionandOutliers

1 Determineandinterpretz–scores.

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Provideanappropriateresponse.

1) Testscoresforastatisticsclasshadameanof79withastandarddeviationof4.5.Testscoresforacalculusclass

hadameanof69withastandarddeviationof3.7.Supposeastudentgetsa66onthestatisticstestanda81on

thecalculustest.Calculatethez–scoreforeachtest.Onwhichtestdidthestudentperformbetterrelativetothe

otherstudentsineachclass?

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

2) Astudentscores56onageographytestand285 onamathematicstest.Thegeographytesthasameanof80

andastandarddeviationof20.Themathematicstesthasameanof300andastandarddeviationof10.Ifthe

dataforbothtestsarenormallydistributed,onwhichtestdidthestudentscorebetterrelativetotheother

studentsineachclass?

A) Thestudentscoredbetteronthegeographytest.

B) Thestudentscoredbetteronthemathematicstest.

C) Thestudentscoredthesameonbothtests.

3) Manyfirmsuseon–the–

obtrainingtoteachtheiremployeesnewsoftware.Supposeyouworkinthepersonnel

departmentofafirmthatjustfinishedtrainingagroupofitsemployeesinnewsoftware,andyouhavebeen

requestedtoreviewtheperformanceofoneofthetraineesonthefinaltestthatwasgiventoalltrainees.The

meanandstandarddeviationofthetestscoresare73and2,respectively,andthedistributionofscoresis

mound–shapedandsymmetric.Supposethetraineeinquestionreceivedascoreof72.Computethetraineeʹs

z–score.

A) z=–0.50 B) z=0.5 C) z= –0.96 D) z=0.96

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4) Aseveredroughtaffectedseveralwesternstatesfor3years.AChristmastreefarmerisworriedaboutthe

droughtʹseffectonthesizeofhistrees.Todecidewhetherthegrowthofthetreeshasbeenretarded,thefarmer

decidestotakeasampleoftheheightsof25treesandobtainsthefollowingresults(recordedininches):

60 57 62 69 46 54 64 60 59 58 75 51 49

67 65 44 58 55 48 62 63 73 52 55 50

Thetreefarmerfeelsthenormalheightofatreethatwasunaffectedbythedroughtwouldbe65inches.Find

thez–scoreforatreethatis65inchestall.

A) z=0.84 B) z=0.98 C) z=0.77 D) z=0.98

5) Atelevisionstationclaimsthattheamountofadvertisingperhourofbroadcasttimehasanaverageof16

minutesandastandarddeviationequalto1.4minutes.Youwatchthestationfor1hour,atarandomly

selectedtime,andcarefullyobservethattheamountofadvertisingtimeisequalto8minutes.Calculatethe

z–scoreforthisamountofadvertisingtime.

A) z=–5.71 B) z=5.71 C) z= –0.41 D) z=0.41

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

6) Astudywasdesignedtoinvestigatetheeffectsoftwovariables–(1)astudentʹslevelofmathematicalanxiety

and(2)teachingmethod–onastudentʹsachievementinamathematicscourse.Studentswhohadalowlevel

ofmathematicalanxietyweretaughtusingthetraditionalexpositorymethod.Thesestudentsobtainedamean

scoreof360andastandarddeviationof50onastandardizedtest.Findandinterpretthez–scoreofastudent

whoscored380onthestandardizedtest.

7) Solarenergyisconsideredbymanytobetheenergyofthefuture.Arecentsurveywastakentocomparethe

costofsolarenergytothecostofgasorelectricenergy.Resultsofthesurveyrevealedthatthedistributionof

theamountofthemonthlyutilitybillofa3–bedroomhouseusinggasorelectricenergyhadameanof$119

andastandarddeviationof$14.Assumingthedistributionismound–shapedandsymmetric,wouldyou

expecttoseea3–bedroomhouseusinggasorelectricenergywithamonthlyutilitybillof$203.00?Explain.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

8) Findthez–scoreforthevalue96

whenthemeanis92 andthestandarddeviationis3.

A) z=1.33 B) z=1.00 C) z= –1.01 D) z=1.01

9) Ahighlyselectiveboardingschoolwillonlyadmitstudentswhoplaceatleast1.5z–scoresabovethemeanona

standardizedtestthathasameanof110andastandarddeviationof12.Whatistheminimumscorethatan

applicantmustmakeonthetesttobeaccepted?

A) 128 B) 92 C) 122 D) 98

10) Apharmaceuticaltestingcompanywantstotestanewcholesteroldrug.Theaveragecholesterolofthetarget

populationis200mgandtheyhaveastandarddeviationof25mg.Thecompanywishedtotestasampleof

peoplewhofallbetween1.5and3z–scoresabovethemean.Intowhatrangemustacandidateʹscholesterol

levelbeinorderforthecandidatetobeincludedinthestudy?

A) 237.5–275 B) 225–237.5 C) 125–162.5 D) 162.5–275

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2 Interpretpercentiles.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Whenresultsfromascholasticassessmenttestaresenttotest–takers,thepercentilesassociatedwiththeir

scoresarealsogiven.Supposeatest–takerscoredatthe99thpercentilefortheirverbalgradeandatthe36th

percentilefortheirquantitativegrade.Interprettheseresults.

A) Thisstudentperformedbetterthan99%oftheothertest–takersintheverbalpartandbetterthan36% in

thequantitativepart.

B) Thisstudentperformedbetterthan99%oftheothertest–takersintheverbalpartandbetterthan64%in

thequantitativepart.

C) Thisstudentperformedbetterthan1%oftheothertest–takersintheverbalpartandbetterthan64%in

thequantitativepart.

D) Thisstudentperformedbetterthan1%oftheothertest–takersintheverbalpartandbetterthan36% in

thequantitativepart.

2) Thepercentageofmeasurementsthatareabovethe39thpercentileis

A) 61% B) 39% C) 71% D) cannotdetermine

3) Thepercentageofmeasurementsthatarebelowthe88thpercentileis

A) 88% B) 12% C) 22% D) cannotdetermine

Usetheogivetosolvetheproblem.

4) Thegraphbelowisanogiveofscoresonamathtest.Theverticalaxisinanogiveisthecumulativerelative

frequencyandcanalsobeinterpretedasapercentile.

PercentileRanksofMathTestScores

10 20 30 40 50 60 70 80 90 100

100

Test Score

Percentile

10 20 30 40 50 60 70 80 90 100

100

Test Score

Percentile

Usethegraphtoapproximatethepercentilerankofanindividualwhosetestscoreis60.

A) 37 B) 70 C) 42 D) 65

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5) Thegraphbelowisanogiveofscoresonamathtest.Theverticalaxisinanogiveisthecumulativerelative

frequencyandcanalsobeinterpretedasapercentile.

PercentileRanksofMathTestScores

10 20 30 40 50 60 70 80 90 100

100

Test Score

Percentile

10 20 30 40 50 60 70 80 90 100

100

Test Score

Percentile

Usethegraphtoapproximatethetestscorethatcorrespondstothe40thpercentile?

A) 62 B) 10 C) 56 D) 15

3 Determineandinterpretquartiles.Checkasetofdataforoutliers.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Thecommutetimes(inminutes)of30employeesarelistedbelow.FindQ3.

31 41 45 48 52 55 56 56 63 65

67 67 69 70 70 74 75 78 79 79

80 81 83 85 85 87 90 92 95 99

A) 83min B) 56min C) 72 min D) 82min

2) Theonewaydistancesfromwork(inmiles)of30employeesarelistedbelow.FindQ3.

25 25 26 26.5 27 27 27.5 28 28 28.5

29 29 30 30 30.5 31 31 32 32.5 32.5

33 33 34 34.5 35 35 37 37 38 38

A) 34mi B) 28mi C) 30.75 mi D) 35mi

3) Healthcareissuesarereceivingmuchattentioninbothacademicandpoliticalarenas.Asociologistrecently

conductedasurveyofcitizensover60yearsofagewhosenetworthistoohightoqualifyforgovernment

healthcarebutwhohavenoprivatehealthinsurance.Theagesof25uninsuredseniorcitizenswereasfollows:

68 73 66 76 86 74 61 89 65 90 69 92 76

62 81 63 68 81 70 73 60 87 75 64 82

FindQ1ofthedata.

A) 65.5 B) 81.5 C) 64.5 D) 66.5

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4) Healthcareissuesarereceivingmuchattentioninbothacademicandpoliticalarenas.Asociologistrecently

conductedasurveyofseniorcitizenswhosenetworthistoohightoqualifyforgovernmenthealthcarebut

whohavenoprivatehealthinsurance.Theagesof25uninsuredseniorcitizenswereasfollows:

71 76 69 79 89 77

64 92 68 93 72 95

79 65 84 66 71 84

73 76 63 90 78 67 85



FindQ1ofthedata.

A) 68.5 B) 68 C) 69 D) 76.5

5) Agroupof79studentswereaskedhowfartheycommutetoworkfromhomeeachtimetheygotoworkfrom

home.Theresultsaregivenbelow.Determinethefirstquartile.

Miles

traveled

Frequency

1 1

2 2

3 12

4 18

5 7

6 10

7 10

8 11

9 5

10 3

A) 4mi B) 3mi C) 5mi D) 6mi

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

6) Theonewaydistancesfromwork(inmiles)of30employeesarelistedbelow.Findtheinterquartilerangeof

the30distanceslistedbelow.

25 25 26 26.5 27 27 27.5 28 28 28.5

29 29 30 30 30.5 31 31 32 32.5 32.5

33 33 34 34.5 35 35 37 37 38 38

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

7) Themonthlytelephoneusage(inminutes)of30adultsislistedbelow.Findtheinterquartilerangeforthe

telephoneusageofthe30adults.

154 156 165 165 170 171 172 180 184 185

189 189 190 192 195 198 198 200 200 200

205 205 211 215 220 220 225 238 255 265

A) 31 B) 30 C) 32 D) 29

8) Thefollowingdataaretheyields,inbushels,ofhayfromafarmerʹslast10years:

375,210,150,147,429,189,320,580,407,180.

FindtheIQR.

A) 227 B) 265 C) 253 D) 279

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SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

9) Tostudythephysicalfitnessofasampleof28people,thedatabelowwerecollectedrepresentingthenumber

ofsit–upsthatapersoncoulddoinoneminute.

10 12 12 15 15 15 18

20 22 25 25 26 29 30

32 33 40 40 40 45 46

47 48 48 50 52 53 56

Determinethelowerandupperfences.Arethereanyoutliersaccordingtothiscriterion?

10) Thesellingpricesofmutualfundschangedaily.Inordertostudythesechanges,asampleofmutualfundswas

examinedandthedailychangesinpricearelistedbelow.

0.05,0.00,–0.03,–0.01,0.18,0.00,0.02,0.29,0.00,–0.07,0.10,0.07,0.03

Determinethelowerandupperfences.Arethereanyoutliersaccordingtothiscriterion?

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

11) Agroupof79studentswereaskedhowfartheycommutetoworkfromhomeeachtimetheygotoworkfrom

home.Theresultsaregivenbelow.Wouldadriveof15milesbeconsideredanoutlier?AnswerYesorNo.

Miles

traveled

Frequency

1 1

2 2

3 12

4 18

5 7

6 10

7 10

8 11

9 5

10 3

A) Yes B) No

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

12) Thenormalmonthlyprecipitation(ininches)forAugustislistedfor20differentU.S.cities.Findanyoutliers

andprovideanexplanationforthem.

0.4 1.0 1.5 1.6 2.0

2.2 2.4 2.7 3.4 3.4

3.5 3.6 3.6 3.7 3.7

3.9 4.1 4.2 4.2 7.0

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3.5 TheFive–NumberSummaryandBoxplots

1 Computethefive–numbersummary.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) Giventhefollowingfive–numbersummary,findtheinterquartilerange.

29, 37, 50, 66, 94

A) 29 B) 50 C) 65 D) 32.5

2) Giventhefollowingfive–numbersummary,findQ3.

2.9, 5.7, 10.0, 13.2, 21.1.

A) 13.2 B) 5.7 C) 10.0 D) 21.1

3) Giventhefollowingfive–numbersummary,findtheIQR.

2.9, 5.7, 10.0, 13.2, 21.1.

A) 7.5 B) 7.1 C) 11.1 D) 18.2

4) AnExcelprintoutofsomedescriptivestatisticsforasetofdataisshownbelow.WhatistheIQR?

A) 15.5 B) 15 C) 38 D) 5.5

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

5) Thefollowingisasampleof19Novemberutilitybills(indollars)fromaneighborhood:

52,62,66,68,72,74,74,76,76,76,78,78,82,84,84,86,88,92,96.Findthefive –numbersummary.

6) Elevenhighschoolteacherswereaskedtogivethenumbersofstudentsintheirclasses.Thesampledata

follows:36,31,30,31,20,19,24,34,21,28,24.Findthefive –numbersummary.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

7) Thefollowingisasampleof19Novemberutilitybills(indollars)fromaneighborhood.Whatisthelargestbill

inthesamplethatwouldnotbeconsideredanoutlier?

52,62,66,68,72,74,76,76,76,78,78,82,84,84,86,88,92,96,110

A) $96 B) $95 C) $88 D) $86

8) Elevenhighschoolteacherswereaskedtogivethenumberofstudentsintheirclasses.Thesampledata

follows.Wouldanyoftheclasssizesbeconsideredanoutlier?AnswerYesorNo.

36,31,30,31,20,19,24,34,21,28,24

A) No B) Yes

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9) Arandomsampleofsalepricesofhomesyieldedthefollowingsummaryinformation:

MIN$41,000 25%:$82,000 Median:$124,000

MAX$276,000 75%:$169,000

Commentonahomethathadasalepriceof$429,000.

A) Thisvaluefallsoutsidetheupperfenceandisconsideredanoutlier.

B) Thissalepricewouldbeexpectedsinceitfallsinsidethelowerandupperfences.

C) Thissalepricefallsbetweenthelowerandupperfences.Itcanbeconsideredapotentialoutlier.

D) Thisvaluefallsoutsideofthethirdquartile,butcannotbeconsideredanoutlier.

2 Drawandinterpretboxplots.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Provideanappropriateresponse.

1) TheboxplotshownbelowwasconstructedinExcelfortheamountofsodathatwaspouredbyafilling

machineinto12–ouncesodacansatalocalbottlingcompany.

Basedontheinformationgivenintheboxplotbelow,whatshapedoyoubelievethedatatohave?

A) skewedtotheleft B) approximatelysymmetric

C) skewedtotheright D) cannotbedetermined

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

2) Thetestscoresof30studentsarelistedbelow.Drawaboxplotthatrepresentsthedata.

31 41 45 48 52 55 56 56 63 65

67 67 69 70 70 74 75 78 79 79

80 81 83 85 85 87 90 92 95 99

3) Thecholesterollevels(inmilligramsperdeciliter)of30adultsarelistedbelow.Drawaboxplotthatrepresents

thedata.

154 156 165 165 170 171 172 180 184 185

189 189 190 192 195 198 198 200 200 200

205 205 211 215 220 220 225 238 255 275

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MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

4) SASwasusedtocomparethehighschooldropoutratesforthe30schooldistrictsinonecityin2010and2012.

Theboxplotsgeneratedforthesedropoutratesareshownbelow.

Comparethecenterofthedistributionsandthevariationofthedistributionsforthetwoyears.

YEAR 2010 2012

A) Dropoutrateshadahigheraveragewithlessvariabilityin2010thanin2012.

B) Dropoutrateshadahigheraveragewithmorevariabilityin2010thanin2012.

C) Dropoutrateshadaloweraveragewithmorevariabilityin2010thanin2012.

D) Dropoutrateshadaloweraveragewithlessvariabilityin2010thanin2012.

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

5) Asurveyof200publicuniversitiesindicatedthatthe25thpercentileoftheyearlytuitioncostoftheuniversities

was$4400andthe75thpercentilewas$7000.Theminimumvaluewas$2000,themedianwas$6000,andthe

maximumwas$10,000.Usethisinformationtoconstructaboxplotfortheyearlytuitioncosts.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

6) Ininterpretingaboxplotofadatasetwenotethatthemedianistotheleftofthecenteroftheboxandtheright

lineislongerthantheleftline.Wecanconcludethat

A) Thedataisskewedright.

B) Thedataisskewedleft.

C) Thedataissymmetric.

D) Skewnessorsymmetrycannotbedeterminedbyaboxplot.

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Ch.3 NumericallySummarizingData

AnswerKey

3.1 MeasuresofCentralTendency

1 Determinethearithmeticmean,median,andmodeofavariablefromrawdata.

2 Explainwhatitmeansforastatistictoberesistant.

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3.2 MeasuresofDispersion

1 Determinetherange,standarddeviation,andvarianceofavariablefromrawdata.

2 UsetheEmpiricalRuletodescribedatathatarebellshaped.

Page79

3 UseChebyshevʹsinequalitytodescribeanysetofdata.

3.3 MeasuresofCentralTendencyandDispersionfromGroupedData

1 Approximatethemeanandstandarddeviationofavariablefromgroupeddata.

2 Computetheweightedmean.

3.4 MeasuresofPositionandOutliers

1 Determineandinterpretz–scores.

Page80

2 Interpretpercentiles.

3 Determineandinterpretquartiles.Checkasetofdataforoutliers.

3.5 TheFive–NumberSummaryandBoxplots

1 Computethefive–numbersummary.

2 Drawandinterpretboxplots.

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